Applying integration by part the first time:

$$\int x^2e^xd{x}=\int x^2d(e^x) = x^2e^x - \int e^xd(x^2)=x^2e^x-2\int xe^xd{x}$$

Now applying the same technique again on the remaining integral:

$$\int xe^xd{x}=\int xd(e^x)=xe^x-\int e^xd{x}=xe^x-e^x+C$$

Combining both gives the final result as

$$\int x^2e^xd{x}=\boxed{(x^2-2x+2)e^x+C}$$